Subgroups — C₂×C₂₃×#1387 #19160194

Order 5888.

614 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#108	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1387	C₂	1	4	yes	maximal, direct product factor
5	C₂²×M₁₆×C₂₃	—	2	1	no	—
6	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
8	C₂×C₂₃×M₃₂	—	2	2	no	—
9	C₂×C₂₃×M₃₂	—	2	1	no	—
10	C₂×C₂₃×M₃₂	C₄	1	4	yes	complemented
11	C₂×C₂₃×M₃₂	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₂₃	—	2	1	no	—
13	C₂×C₂₃×#108	—	2	1	no	—
14	C₂×C₂₃×#108	—	2	2	no	—
15	C₂×C₂₃×#108	C₄	1	4	yes	complemented
16	C₂×C₂₃×#108	C₂²	1	2	yes	—
17	C₂×C₂₃×#107	—	2	1	no	—
18	C₂×C₂₃×#107	—	2	1	no	—
19	C₂×C₂₃×#107	—	2	1	no	—
20	C₂×C₂₃×#107	C₄	1	2	yes	—
21	C₂×C₂₃×#107	C₄	1	2	yes	—
22	C₂×C₂₃×#107	C₂²	1	2	yes	—
23	C₂³×C₄×C₂₃	—	4	1	no	—
24	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
25	C₂×M₁₆×C₂₃	—	2	4	no	—
26	C₂×M₁₆×C₂₃	—	2	2	no	—
27	C₂×M₁₆×C₂₃	—	4	1	no	—
28	C₂×M₁₆×C₂₃	—	4	2	no	—
29	C₂²×C₈×C₂₃	—	4	1	no	—
30	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₂₃	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₂₃	D₄	1	2	yes	—
38	C₂²×C₈×C₂₃	Q₈	1	2	yes	—
39	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
42	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
43	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
44	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
45	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
46	C₂₃×M₃₂	—	2	4	no	—
47	C₂₃×M₃₂	—	2	2	no	—
48	C₂₃×M₃₂	C₂×C₄	1	4	yes	complemented
49	C₂×C₁₆×C₂₃	—	2	4	no	—
50	C₂×C₁₆×C₂₃	—	2	2	no	—
51	C₂₃×#108	—	2	4	no	—
52	C₂₃×#108	—	2	2	no	—
53	C₂₃×#108	C₂×C₄	1	4	yes	complemented
54	C₂₃×#107	—	2	2	no	—
55	C₂₃×#107	—	2	2	no	—
56	C₂₃×#107	—	2	2	no	—
57	C₂₃×#107	C₂×C₄	1	4	yes	—
58	C₂⁴×C₂₃	SD₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₂₃	—	4	2	no	—
60	C₂²×C₄×C₂₃	—	4	2	no	—
61	C₂²×C₄×C₂₃	—	4	2	no	—
62	C₂²×C₄×C₂₃	—	8	4	no	—
63	C₂²×C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
64	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₂₃	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
68	C₂²×C₄×C₂₃	D₈	1	1	yes	characteristic
69	C₂²×C₄×C₂₃	SD₁₆	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₂₃	Q₁₆	1	2	yes	—
72	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
73	M₁₆×C₂₃	—	2	4	no	—
74	M₁₆×C₂₃	—	4	4	no	—
75	M₁₆×C₂₃	—	4	2	no	—
76	C₂×C₈×C₂₃	—	4	4	no	—
77	C₂×C₈×C₂₃	—	4	2	no	—
78	C₂×C₈×C₂₃	C₄²	1	2	yes	—
79	C₂×C₈×C₂₃	C₄²	1	2	yes	—
80	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
83	C₂×C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
84	C₂×C₈×C₂₃	C₂²⋊C₄	1	2	yes	—
85	C₂×C₈×C₂₃	C₄⋊C₄	1	2	yes	—
86	C₂×C₈×C₂₃	C₄⋊C₄	1	2	yes	—
87	C₂×C₈×C₂₃	C₄⋊C₄	1	2	yes	—
88	C₂×C₈×C₂₃	C₄⋊C₄	1	2	yes	—
89	C₂×C₈×C₂₃	C₄⋊C₄	1	2	yes	—
90	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
94	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₂₃	C₂×Q₈	1	1	yes	characteristic
96	C₄⋊C₄×C₂₃	—	2	4	no	—
97	C₄⋊C₄×C₂₃	—	4	2	no	—
98	C₄⋊C₄×C₂₃	—	4	2	no	—
99	C₄⋊C₄×C₂₃	—	4	2	no	—
100	C₁₆×C₂₃	—	2	4	no	—
101	C₂×#1387	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂³×C₂₃	—	2	2	no	—
103	C₂³×C₂₃	—	2	2	no	—
104	C₂³×C₂₃	#102	1	1	yes	characteristic
105	C₂³×C₂₃	#102	1	1	yes	characteristic
106	C₂³×C₂₃	#103	1	2	yes	—
107	C₂³×C₂₃	#106	1	2	yes	—
108	C₂³×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
109	C₂×C₄×C₂₃	—	4	4	no	—
110	C₂×C₄×C₂₃	—	8	4	no	—
111	C₂×C₄×C₂₃	—	8	4	no	—
112	C₂×C₄×C₂₃	—	8	4	no	—
113	C₂×C₄×C₂₃	#95	1	2	yes	—
114	C₂×C₄×C₂₃	#95	1	2	yes	—
115	C₂×C₄×C₂₃	#102	1	1	yes	characteristic
116	C₂×C₄×C₂₃	#102	1	1	yes	characteristic
117	C₂×C₄×C₂₃	#102	1	2	yes	—
118	C₂×C₄×C₂₃	#102	1	2	yes	—
119	C₂×C₄×C₂₃	#103	1	2	yes	—
120	C₂×C₄×C₂₃	#103	1	2	yes	—
121	C₂×C₄×C₂₃	#103	1	2	yes	—
122	C₂×C₄×C₂₃	#106	1	2	yes	—
123	C₂×C₄×C₂₃	#107	1	2	yes	—
124	C₂×C₄×C₂₃	#107	1	2	yes	—
125	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
129	C₂×C₄×C₂₃	C₂×SD₁₆	1	1	yes	characteristic
130	C₂×C₄×C₂₃	C₂×Q₁₆	1	1	yes	characteristic
131	C₈×C₂₃	—	4	4	no	—
132	C₈×C₂₃	#95	1	2	yes	—
133	C₈×C₂₃	#95	1	2	yes	—
134	C₈×C₂₃	C₂×C₄²	1	1	yes	characteristic
135	C₈×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₈×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₈×C₂₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂²×M₃₂	C₂×C₂₃	1	1	yes	characteristic
139	C₂²×#108	C₂×C₂₃	1	1	yes	characteristic
140	C₂²×#107	C₂×C₂₃	1	1	yes	characteristic
141	#1387	C₂×C₂₃	1	4	yes	direct product factor
142	C₂²×C₂₃	—	2	1	no	—
143	C₂²×C₂₃	—	2	1	no	—
144	C₂²×C₂₃	—	2	1	no	—
145	C₂²×C₂₃	—	2	1	no	—
146	C₂²×C₂₃	—	2	4	no	—
147	C₂²×C₂₃	—	2	4	no	—
148	C₂²×C₂₃	#340	1	2	yes	—
149	C₂²×C₂₃	#340	1	2	yes	—
150	C₂²×C₂₃	#361	1	2	yes	—
151	C₂²×C₂₃	#362	1	2	yes	—
152	C₂²×C₂₃	C₂×#102	1	1	yes	characteristic
153	C₂²×C₂₃	C₂×#103	1	1	yes	characteristic
154	C₂²×C₂₃	C₂×#106	1	1	yes	characteristic
155	C₄×C₂₃	—	8	4	no	—
156	C₄×C₂₃	#340	1	2	yes	—
157	C₄×C₂₃	#340	1	2	yes	—
158	C₄×C₂₃	C₂×#95	1	1	yes	characteristic
159	C₄×C₂₃	C₂×#102	1	1	yes	characteristic
160	C₄×C₂₃	C₂×#103	1	1	yes	characteristic
161	C₄×C₂₃	C₂×#107	1	1	yes	characteristic
162	C₂²×M₁₆	—	2	1	no	—
163	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	—	2	1	no	—
165	C₂×M₃₂	—	2	2	no	—
166	C₂×M₃₂	—	2	1	no	—
167	C₂×M₃₂	C₄×C₂₃	1	4	yes	complemented
168	C₂×M₃₂	C₂²×C₂₃	1	2	yes	—
169	C₂²×C₁₆	—	2	1	no	—
170	C₂×#108	—	2	1	no	—
171	C₂×#108	—	2	2	no	—
172	C₂×#108	C₄×C₂₃	1	4	yes	complemented
173	C₂×#108	C₂²×C₂₃	1	2	yes	—
174	C₂×#107	—	2	1	no	—
175	C₂×#107	—	2	1	no	—
176	C₂×#107	—	2	1	no	—
177	C₂×#107	C₄×C₂₃	1	2	yes	—
178	C₂×#107	C₄×C₂₃	1	2	yes	—
179	C₂×#107	C₂²×C₂₃	1	2	yes	—
180	C₂×C₂₃	—	2	2	no	—
181	C₂×C₂₃	—	2	1	no	—
182	C₂×C₂₃	—	2	1	no	—
183	C₂×C₂₃	#1387	1	4	yes	direct product factor
184	C₂×C₂₃	C₂×#340	1	1	yes	characteristic
185	C₂×C₂₃	C₂×#361	1	1	yes	characteristic
186	C₂×C₂₃	C₂×#362	1	1	yes	characteristic
187	C₂³×C₄	—	4	1	no	—
188	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
189	C₂×M₁₆	—	2	4	no	—
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	4	1	no	—
192	C₂×M₁₆	—	4	2	no	—
193	C₂²×C₈	—	4	1	no	—
194	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
195	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
196	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
197	C₂²×C₈	C₂×C₄×C₂₃	1	2	yes	—
198	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
199	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
200	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
201	C₂²×C₈	D₄×C₂₃	1	2	yes	—
202	C₂²×C₈	Q₈×C₂₃	1	2	yes	—
203	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	4	1	no	—
208	C₂×C₄⋊C₄	—	4	1	no	—
209	C₂×C₄⋊C₄	—	4	1	no	—
210	M₃₂	—	2	4	no	—
211	M₃₂	—	2	2	no	—
212	M₃₂	C₂×C₄×C₂₃	1	4	yes	complemented
213	C₂×C₁₆	—	2	4	no	—
214	C₂×C₁₆	—	2	2	no	—
215	#108	—	2	4	no	—
216	#108	—	2	2	no	—
217	#108	C₂×C₄×C₂₃	1	4	yes	complemented
218	#107	—	2	2	no	—
219	#107	—	2	2	no	—
220	#107	—	2	2	no	—
221	#107	C₂×C₄×C₂₃	1	4	yes	—
222	C₂₃	C₂×#1387	1	1	yes	characteristic, direct product factor, Sylow
223	C₂⁴	SD₁₆×C₂₃	1	1	yes	characteristic
224	C₂²×C₄	—	4	2	no	—
225	C₂²×C₄	—	4	2	no	—
226	C₂²×C₄	—	4	2	no	—
227	C₂²×C₄	—	8	4	no	—
228	C₂²×C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
229	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
230	C₂²×C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
231	C₂²×C₄	C₄⋊C₄×C₂₃	1	2	yes	—
232	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
233	C₂²×C₄	D₈×C₂₃	1	1	yes	characteristic
234	C₂²×C₄	SD₁₆×C₂₃	1	1	yes	characteristic
235	C₂²×C₄	SD₁₆×C₂₃	1	2	yes	—
236	C₂²×C₄	Q₁₆×C₂₃	1	2	yes	—
237	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
238	M₁₆	—	2	4	no	—
239	M₁₆	—	4	4	no	—
240	M₁₆	—	4	2	no	—
241	C₂×C₈	—	4	4	no	—
242	C₂×C₈	—	4	2	no	—
243	C₂×C₈	C₄²×C₂₃	1	2	yes	—
244	C₂×C₈	C₄²×C₂₃	1	2	yes	—
245	C₂×C₈	C₂²⋊C₄×C₂₃	1	2	yes	—
246	C₂×C₈	C₂²⋊C₄×C₂₃	1	2	yes	—
247	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
248	C₂×C₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
249	C₂×C₈	C₂²⋊C₄×C₂₃	1	2	yes	—
250	C₂×C₈	C₄⋊C₄×C₂₃	1	2	yes	—
251	C₂×C₈	C₄⋊C₄×C₂₃	1	2	yes	—
252	C₂×C₈	C₄⋊C₄×C₂₃	1	2	yes	—
253	C₂×C₈	C₄⋊C₄×C₂₃	1	2	yes	—
254	C₂×C₈	C₄⋊C₄×C₂₃	1	2	yes	—
255	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
256	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
257	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
258	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
259	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
260	C₂×C₈	C₂×Q₈×C₂₃	1	1	yes	characteristic
261	C₄⋊C₄	—	2	4	no	—
262	C₄⋊C₄	—	4	2	no	—
263	C₄⋊C₄	—	4	2	no	—
264	C₄⋊C₄	—	4	2	no	—
265	C₁₆	—	2	4	no	—
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	C₂₃×#102	1	1	yes	characteristic
269	C₂³	C₂₃×#102	1	1	yes	characteristic
270	C₂³	C₂₃×#103	1	2	yes	—
271	C₂³	C₂₃×#106	1	2	yes	—
272	C₂³	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
273	C₂×C₄	—	4	4	no	—
274	C₂×C₄	—	8	4	no	—
275	C₂×C₄	—	8	4	no	—
276	C₂×C₄	—	8	4	no	—
277	C₂×C₄	C₂₃×#95	1	2	yes	—
278	C₂×C₄	C₂₃×#95	1	2	yes	—
279	C₂×C₄	C₂₃×#102	1	1	yes	characteristic
280	C₂×C₄	C₂₃×#102	1	1	yes	characteristic
281	C₂×C₄	C₂₃×#102	1	2	yes	—
282	C₂×C₄	C₂₃×#102	1	2	yes	—
283	C₂×C₄	C₂₃×#103	1	2	yes	—
284	C₂×C₄	C₂₃×#103	1	2	yes	—
285	C₂×C₄	C₂₃×#103	1	2	yes	—
286	C₂×C₄	C₂₃×#106	1	2	yes	—
287	C₂×C₄	C₂₃×#107	1	2	yes	—
288	C₂×C₄	C₂₃×#107	1	2	yes	—
289	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
290	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
291	C₂×C₄	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
292	C₂×C₄	C₂×D₈×C₂₃	1	1	yes	characteristic
293	C₂×C₄	C₂×SD₁₆×C₂₃	1	1	yes	characteristic
294	C₂×C₄	C₂×Q₁₆×C₂₃	1	1	yes	characteristic
295	C₈	—	4	4	no	—
296	C₈	C₂₃×#95	1	2	yes	—
297	C₈	C₂₃×#95	1	2	yes	—
298	C₈	C₂×C₄²×C₂₃	1	1	yes	characteristic
299	C₈	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
300	C₈	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
301	C₈	C₂×C₄⋊C₄×C₂₃	1	1	yes	characteristic
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	C₂₃×#340	1	2	yes	—
309	C₂²	C₂₃×#340	1	2	yes	—
310	C₂²	C₂₃×#361	1	2	yes	—
311	C₂²	C₂₃×#362	1	2	yes	—
312	C₂²	C₂×C₂₃×#102	1	1	yes	characteristic
313	C₂²	C₂×C₂₃×#103	1	1	yes	characteristic
314	C₂²	C₂×C₂₃×#106	1	1	yes	characteristic
315	C₄	—	8	4	no	—
316	C₄	C₂₃×#340	1	2	yes	—
317	C₄	C₂₃×#340	1	2	yes	—
318	C₄	C₂×C₂₃×#95	1	1	yes	characteristic
319	C₄	C₂×C₂₃×#102	1	1	yes	characteristic
320	C₄	C₂×C₂₃×#103	1	1	yes	characteristic
321	C₄	C₂×C₂₃×#107	1	1	yes	characteristic
322	C₂	—	2	2	no	—
323	C₂	—	2	1	no	—
324	C₂	—	2	1	no	—
325	C₂	C₂₃×#1387	1	4	yes	direct product factor
326	C₂	C₂×C₂₃×#340	1	1	yes	characteristic
327	C₂	C₂×C₂₃×#361	1	1	yes	characteristic
328	C₂	C₂×C₂₃×#362	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	#102
commutator	C₈	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₈	C₂³×C₂₃
prime radical	C₂⁴×C₂₃	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ C₂³×C₈×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂₃×#1387	C₂	direct (N × H)
10. C₂×C₂₃×M₃₂	C₄	semidirect
15. C₂×C₂₃×#108	C₄	semidirect
48. C₂₃×M₃₂	C₂×C₄	semidirect
53. C₂₃×#108	C₂×C₄	semidirect
101. C₂×#1387	C₂₃	direct (N × H)
141. #1387	C₂×C₂₃	direct (N × H)
167. C₂×M₃₂	C₄×C₂₃	semidirect
172. C₂×#108	C₄×C₂₃	semidirect
183. C₂×C₂₃	#1387	direct (N × H)
212. M₃₂	C₂×C₄×C₂₃	semidirect
217. #108	C₂×C₄×C₂₃	semidirect
222. C₂₃	C₂×#1387	direct (N × H)
325. C₂	C₂₃×#1387	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂₃×M₃₂	2
C₂²×C₂₃×#108	2
C₂²×C₂₃×#107	2
C₂₃×#1387	2
C₂×#1387	23

Subgroups — C2×C23×#1387 #19160194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#1387 #19160194